Bending Energetics of Tablet‐Shaped Micelles: A Novel Approach to Rationalize Micellar Systems

A novel approach to rationalize micellar systems is expounded in which the structural behavior of tablet‐shaped micelles is theoretically investigated as a function of the three bending elasticity constants: spontaneous curvature (H₀), bending rigidity (k_c), and saddle‐splay constant (k?_c). As a result, experimentally accessible micellar properties, such as aggregation number, length‐to‐width ratio, and polydispersity, may be related to the different bending elasticity constants. It is demonstrated that discrete micelles or connected cylinders form when H₀>1/4ξ, where ξ is the thickness of a surfactant monolayer, whereas various bilayer structures are expected to predominate when H₀<1/4ξ. Our theory predicts, in agreement with experiments, a transition from discrete globular (tablet‐shaped) micelles to a phase of ordered, or disordered, connected cylinders above a critical surfactant concentration. Moreover, a novel explanation for the mechanism of growth, from small globular to long rodlike or wormlike micelles, follows as a consequence from the theory. In accordance, polydisperse elongated micelles (large length‐to‐width ratio) form as the bending rigidity is lowered, approaching the critical point at k_c=0, whereas monodisperse globular micelles (small length‐to‐width ratio) are expected to be present at large k_c values. The spontaneous curvature mainly determines the width of tablet‐shaped or ribbonlike micelles, or the radius of disklike micelles, whereas the saddle‐splay constant primarily influences the size but not the shape of the micelles.